[{_id:0,user_id:12,list:[{_id:0,name:"john"},{_id:1,name:"hanna"}]},{_id:1,user_id:22,list:[{_id:0,name:"john"},{_id:1,name:"hanna"}]}]

db.collection.find({user_id:12},{list:{$first:{$filter:{input:"$list",cond:{$eq:["$$this.name","john"]}}}}})